There is a good chance the hoa is set up in a way that the tax for the "common" area is distributed equally on all the parcels occupied by homes.
There is an equally good chance MI law says no adverse possession can be demonstrated on property that has had it's tax payed.
If there has been no nusiance (trash, weeds, homeless camps, etc.) on that area and it is basically green-belt or riparian reserve the hoa lawyer may be milking the hoa. My gut feeling is the case should be tossed and damages should be sought from the claimant.
Again, the planning process files and the recorded map are a start.